Profit maximisation and supply (L6)

Main source: NS ch 8

8.2 Profit maximisation
8.3 Marginal revenue
includes trivial perfect competition case and ‘monopoly’ case
8.4 Marginal revenue curve
8.5 Supply decisions of a price-taking firm

Practical questions

What makes sense?

We should set the price that maximises our revenue

We are at the point where if we raise our price by 10% sales will fall by 5%, so we better not do it!

???

We reduced our price to £1000 this year and we were able to sell 10 units more this year than last year. These only cost us £500 to make, so we are better off.

???

We should stop producing immediately, because the market price has fallen below our average costs, if we take into account our yearly license fee

???

Key goals of this chunk

What is ‘marginal revenue’, why is
- $MR\leq p$ for firm facing downward sloping demand?
- but $MR= p$ for a price-taking firm

Price and output choice (condition) for a price-taking firm
- firm’s shut-down/entry decision
- what is a ‘price-taking firm’?

Context

We considered production functions
… cost and cost minimization
- … expansion paths

Production functions, prices $\rightarrow$ cost of production …

Now: “what output to set to max profits?”

Next: consequences for the market

Marginal revenue

Marginal revenue: The additional gross income a firm gains from increasing the quantity it supplies by one unit

Q: Impact of increasing quantity?

It can sell an additional unit at some price

But it may have to reduce prices on all units to do this (more on this later)

MR for firm facing ‘downward-sloping demand’

Single price $\rightarrow$ sell more only by reducing price on all units
- E.g., sell 51 units rather than 50 by reducing price from 1 to 0.99

MR $<$ market price here because
Get (new) market price for additional unit $\rightarrow$ + 0.99

But lose 0.01 on all previous 50 units $\rightarrow$ - 0.50
So MR is 0.49

MR curves be like:

Price-taker

MR for a price-taking firm

A price-taking firm (perfect competition):

gets market price P for each additional unit

the firm is small, so its output has (virtually) no impact on P

Thus its marginal revenue is constant at $P$

Profit-maximisation

Operating? $\rightarrow$ Set optimal output $q^*$

… profit-maximising output: at the (unique) $q^*$ such that $MR=MC$

…if this exists

Holds for all firms

Market power (‘price-setters’): MR declining (down-sloping ‘demand’)

Price-takers: setting $MR(q)=MC(q)$ means setting $P=MC(q)$, bc $P=MR(q)$

For a firm with market power:

For a firm with market power:

Supply decisions of a price-taking firm

Price-taking firms: what price?

Can sell all output at market price P. Will price at P.

Set P<P* $\rightarrow$?

Sell same amount, earn less. … Not smart!

Set P>P*?

Sell no units. Smooth move, hotshot!

Price-taking firms: How much to produce?

(Draw)

Standard assumption: $MC(0)<P^*$, $MC(q)$ increasing in q … or at least there’s some region for which AVC< $P^*$

Thus choose q for which $MC(q) = P^*$ $\rightarrow$ ‘Perfectly competitive firms price at marginal cost’

But…

But if P* below your average cost for any possible output q $\rightarrow$ shut down!

If P* below ‘(SR) average variable costs’ $\rightarrow$ shut down immediately.

If P* $<$ LRAC $\rightarrow$ shut down before incurring further FC.

Some revision questions

From 2017 final exam

A firm that sought to maximize revenue (rather than profit) would choose to produce an output level for which marginal revenue was equal to

1. marginal cost
1. average cost.
1. price.
1. zero.
1. as high as possible.

Choose all that apply: If the demand faced by a firm is elastic (but not perfectly elastic), selling one less unit of output will

1. decrease revenue.
1. keep revenues constant.
1. require a decreased price.
1. increase revenue.
1. allow an increased price.

Perfect competition in a single market (L7)

Main source: NS Ch 9

Key goals of this chunk

How firms’ supply curves aggregate to the market supply curve
What is a ‘perfectly competitive market’?

Motivating questions:

With many ‘price taking firms’, how does aggregate supply respond to changes in demand?
Can such firms make a profit in the short run? In the long run?

Importance of entry /& exit, implications for short & long run:
LR market supply curve: what it looks like & why

…

Consumer surplus, producer surplus, implications for welfare analysis
Pareto Optimality

Basic argument: why perfectly competitive market $\rightarrow$ Pareto Optimal outcome (under certain conditions)
Critiques of this, idea of ‘market failure’

Consider: Should price-taking firms and perfect competition be our ‘baseline’ dominant model?

Reasonable to assume?

Free entry of firms/no ‘barriers’?
Homogenous products?
Decreasing returns to scale at some point?

Deep political/philosophical question:

Should we expect ‘chaotic competition’ to lead to the most efficient outcomes, and if so, when and under what conditions?

Better to restrict the entry of firms (single firm with a guaranteed monopoly?)
Better to regulate prices?

Urgent question: Brexit

Trade with Europe may default to WTO terms

$\rightarrow$ Very large tariffs on some goods, ‘non-tariff barriers’ on others

UK (and EU) firms: Unknown impact on input prices, demand curves, competition, etc.

Can ‘GE models’ help predict these and help firms plan and reoptimise?
How long will it take to return to some ‘equilibrium’?

Fewer firms in UK markets $\rightarrow$ less competition $\rightarrow$ loss of consumer surplus?

Also, … many new regulations bundled with new trade deals:

Which are ‘pro-competitive’ or redress market failures and which restrain trade?

SKIP: Pricing in the very short run

SR supply

For a further revision, ‘firms in competitive markets’ is well mapped out in a step-by step Powerpoint you can download:

http://web.mnstate.edu/stutes/notes/mankiwjustpp/firms_competitive.ppt

(start from beginning, this is specifically referred to beginning on slide 17; use ‘presentation mode’)

We will quickly outline:

SR: Number of firms in the market is fixed: no entry/exit

Demand shifts $\rightarrow$ prices change $\rightarrow$ existing firms adjust quantities supplied

Market supply curve: sum each firm’s supply curve

Recall: Under perfect competition each firm

charges market price $P^*$
produces q at a point where $mc(q)=p^*$
- as long as there’s some output q where $AC \leq P*$

Thus, for every price $P^{*}$, it produces $q$ where $mc(q)=P^{*}$.

$\rightarrow$ its mc curve is its supply curve!

Except where $AC(q)>p^*$ for all q $\rightarrow$ it produces zero

Sum each firm’s supply curve horizontally

SR Price determination

(Read at home: handout, text)

Sum across firms (mc curve where $>$ AC curves) $\rightarrow$ market supply curve

Sum individual demand curves $\rightarrow$ market demand curve

Where do these intersect?

At this price $P^*$ we have $Q_d(P^*)=Q_s(P^*)$ $\rightarrow$ the ‘short run equilibrium price’

$P^* > AC$ possible in the short run

$\rightarrow$ can make SR economic profits!

Illustration of SR price determination

Avoid confusion: The market demand curve is downward sloping. The demand curve for an individual firm under perfect competition is effectively horizontal.

Price acts as a signal, leading to efficient choices:

to firms, telling them ‘how much to produce’

Price signal, leading to efficient choices:

to consumers, how much to purchase

and ‘which consumers should obtain the units produced’?

Read on your own: shifts in S and D curves

The Long run

Draw it: Long run equilibrium response to a demand shift, constant-cost case (ignore SMC)

The Long run

In LR ‘free entry and exit’ of firms, many firms have access to same production process

Suppose positive economic profits in industry (for efficient producers)

I.e., $P^*>AC(q)$ for some q

$\rightarrow$ Firms enter $\rightarrow$ Supply curve shifts out

$\rightarrow$ equilibrium price declines $\rightarrow$ profits decline

Repeat until economic profit falls to zero, i.e., until $P^*=AC(q)$ for the minimum AC q

Now suppose negative economic profits in industry (for efficient producers)

I.e., $P^*<AC(q)$ for any q

$\rightarrow$ Firms exit $\rightarrow$ Supply curve shifts inwards

$\rightarrow$ equilibrium price rises $\rightarrow$ profits rise

Repeat until economic profit rises to zero; i.e., until $P^*=AC(q)$ for the minimum AC q

Long Run Equilibrium

Firms choose output to max profit

Profit max: $P^* = MC(q)$

No firms in the market want to exit, no firms outside want to enter

Zero economic profits:

$P^* = AC(q)$

Also, with free entry/exit…

all firms (in) produce $q$ that minimizes their AC, and all same average cost

I.e., $P^\ast = min[AC(q)] = MC(q)$ for any firm in the market
I.e., MC curve intersects AC curve at its minimum.
- and it’s the same AC for all firms

Why?

Why $P* = min [ac(q)] = mc(q)$?

No profit in equilibrium and firms choose q so that $P^\ast=mc(q)$

$\rightarrow$ $P^\ast = AC(q) = MC(q)$ for all firms (in the market)

Suppose a firm produced at a point above it’s minimum AC,

i.e., if $AC(q)> min [AC(q)]$

$\rightarrow$ it could profit by producing at the q that minimised its AC (contradicting above)

… so would other firms, who’d be induced to enter; so that couldn’t have been an equilibrium

Long Run (LR) Supply

2019: This curve itself is not covered on the midterm, so we may skip it for now

We have the SR supply curve (upward sloping)
But we know that in the LR this will shift out in response to a price change

$\rightarrow$ Taking this shift into account gives us the Long Run Supply Curve

LR supply curve looks like?

Demand curve shifts out $\rightarrow$ price rise $\rightarrow$ firms enter
… do firms produce at the same minimum AC as before?

Depends:

Does entry/higher production change cost function?

So input costs rise?

‘Externalities’ between firms, consumers’ (e.g., network externalities)

Long run population and economic growth $\rightarrow$ ?

As the economy grows, which items will get relatively more expensive?

LR Supply: Constant cost case

LR Supply: Increasing cost case

Long-run elasticity of supply: % change in LR $Q^s$ / % change P

(Various estimates over the years, see NS text)

Consumer and producer surplus, efficiency

Consumer surplus (reprise): Extra value … from consuming good over its price. WTP for right to consume a good at its current price.

Area between the demand curve and the market price

Producer surplus: Value producers get for a good less the opportunity costs they incur by producing it. What producers would pay for right to sell good at current market price. (Essentially profits not counting FC.)

Area between supply curve and market price

In LR, zero-profits, all costs are variable $\rightarrow$ producer surplus is zero

In what sense is a competitive market ‘efficient’?

Roughly; single-market depiction

Allocation of resources maximizes total surplus

Total surplus $=$ consumer $+$ producer surplus

At market equilibrium: no more mutually-beneficial exchanges can be made

‘A competitive market in equilibrium will max total surplus’

We can use these models/concepts to consider…

‘Who suffers from a tax’ in the LR and SR?

Who gains from technological innovation?

Who gains and who is harmed by trade restrictions, and do the costs outweigh the benefits?

Today’s goals (28 Oct 2019)

General equilibrium and efficiency – key principles and arguments

What is ‘Pareto efficiency?’
What conditions must hold for an economy to achieve this?
Basic story for why efficiency should attain
First and second welfare theorems
Market failures

Market failure: one case - Public goods

How do we define a ‘public good’… what are some examples?
Basic argument for market failure here

Second annual pre-midterm championship (revision)

Additional material on efficiency: key principles

General equilibrium and efficiency: Coverage

This is a very brief excerpt and summary of the material in NS chapter 10, with some additional motivation. If you understand these slides/notes you don’t have to read chapter 10.

Key principles: efficiency & ‘general’ equilibrium

Under certain conditions competitive markets are efficient in equilibrium

But:

Some markets may not reach equilibrium ‘quickly’

These conditions may not hold $\rightarrow$ market failure

Efficiency itself doesn’t imply preferred outcomes: can involve a great deal of inequality

General Equilibrium (GE) analysis: entire economy as a system of interacting, interdependent markets

GE: Set of prices s.t. $Q_s(P)=Q_d(P)$ in all markets, including input markets

Overall Pareto efficiency: no one can be made better off without making someone else worse off

Why is this how we define efficiency?

Because if we could do so, we would not be at an efficient point

Overall efficiency requires three conditions:

Efficiency in production (being on the PPF): No way to reallocate inputs to increase production of one good without reducing production of another

Given society’s resources, we are producing ‘as much as possible’

Efficiency in production?

Formal argument: efficiency in production

Specifically, economy produces on the PPF: given available inputs, we produce ‘as much as possible’

I.e., we can’t produce more of any good without producing less of some other good

$\leftarrow$ Ensured by ‘efficient use of inputs’ (same ‘bang for the buck’ per input for all firms and products)

$\leftarrow$ Ensured by ‘competitive market for inputs’ (all firms face the same prices, prices set to equalise demand and supply for inputs)

Efficiency in consumption (exchange efficiency): No way to reallocate output amongst consumers to make them all better off

Given what we’re producing, it is going to the ‘right consumers’.

Edgeworth box scavenger hunt

Does this look familiar? Where can you find it at Exeter? What does it mean?

Formal conditions and argument for efficiency in consumption (Exchange efficiency)

Specifically: No way to reallocate output amongst consumers to make them all better off

With DMRS, this is equivalent to ‘for the last (positive) unit of X purchased by each consumer, they are all willing to give up the same amount of X to get another Y’

I.e., their marginal rates of substitution for the last unit they buy are all the same: equal to the price ratio.

$\leftarrow$ basically ensured by the $MRS(x,y)=p_x/p_y$ ‘bang for the buck’ condition.

Given our inputs, we can produce ‘efficiently’, i.e, along the PPF,

and given the amounts of each good produced, it is ‘consumed by the right people’ (no more room for trade) …

yet we may still not be at efficiency? Why not?

We need to produce the right combination of goods.

Efficient allocation of resources (‘top-level’ condition): No way to produce more of one good and less of another to make all consumers better off

Formal conditions/argument for top-level cond.

Efficiency $\leftarrow$ (Along PPF), can’t adjust product mix to make any consumers better off without making some worse off

Formally:

DMRT on x PPF & DMRS for consumers (rem: all have same MRS) …

$\leftrightarrow MRS(x,y)=MRT(x,y)$ is necessary/sufficient for top-level efficiency

I.e., marginal tradeoff in production = marginal tradeoff in consumption, i.e., Slope of PPF at chosen point = slope of everyone’s indifference curve at their chosen point

Need \[MRS(x,y)=MRT(x,y)\] for top-level efficiency.

Why should the free-market lead to this?

Optimizing consumers, free exchange $\rightarrow$ MRS reflects relative prices

competitive firms choose q’s s.t. $mc(q_x)=p_x$ $\forall$ firms, goods

$\rightarrow$ ratios are equal; consumers’ value tradeoff equals production tradeoff :)

First fundamental theorem of welfare economics: A general competitive equilibrium is Pareto efficient, under standard assumptions

Intuition: free exchange leaves no room for mutually-beneficial improvements, and firms and consumers optimise

Second fundamental theorem: Under some fancy assumptions, any Pareto efficient outcome is a competitive equilibrium for some pattern of initial endowments

So if we could costlessly redistribute endowments, we could attain any socially-desirable outcome by doing so, and then relying on the free market.

First fundamental theorem of welfare economics: A general competitive equilibrium is Pareto efficient, under standard assumptions.

But these assumptions may not hold $\rightarrow$ ‘market failures’

Imperfect Competition

Markets not competitive, because of barriers to entry or increasing returns to scale
$\rightarrow$ Prices won’t reflect marginal costs $\rightarrow$ ‘deadweight losses’

Externalities, public goods, altruism

Assumptions: ‘anything someone values’ is bought & sold in the market on their own behalf

But:

Externalities: All costs (& benefits) may not be priced; e.g., pollution
Public goods (and bads): Many benefit from the same good (e.g., fireworks)

Also: Altruism/interdependent utilities: People care about others’ consumption

Asymmetric information: People have different information about the state of the world (costs, risks, a good’s quality…)

Bounded rationality: people may not choose in their own best interests

Second Welfare theorem

If we could costlessly redistribute endowments, we could attain any socially-desirable outcome

by redistributing and then relying on the free market

But:

Redistribution via ‘optimal lump-sum’ taxes isn’t easy, as endowments may be unobservable
and redistribution based on things you can affect, e.g. income, may distort incentives.

Practice question on GE/efficiency

Choose one or all that are correct. The following situation(s) or condition(s) imply the economy has NOT attained a Pareto efficient outcome.

A. We can produce more toothbrushes w/o producing less toothpaste, but this requires us to produce less food; all 3 goods are valued by consumers.

B. The economy is not producing any liverwurst; however, liverwurst does not enter into any consumer’s utility function.

C. At the current levels of consumption, older people are willing to give up 2 toothbrushes for 1 toothpaste, while younger people are willing to trade these off 1-for-1; both groups have a positive amount of each.

D. At current production, the PPF implies we could produce one fewer tube of toothpaste and thus produce two more toothbrushes; however, all consumers have a MRS of 1 between these two goods, and are consuming a positive amount of both.

Some key things for midterm (recap)

How do economists measure and test models,
- techniques and terms used
- thoughts on estimating demand and supply curves

The ‘axioms’ over preferences, the justification for these, and what they imply for utility functions

Understand indifference curves and budget constraints well

Conditions for consumer optimisation (obviously this is important) including for when a consumer will choose to consume none of a good

Definitions of ‘types of goods’ as implied by characteristics of the demand function
Impacts of price changes (own good, other good) and income on an individual’s consumption, and what goes into this and how to depict it.
(Producer and) consumer surplus.

‘Applications’, especially those discussed both in the assigned text and in the lectures.

Firm’s conditions for optimisation in input choice.
Firm’s conditions for ‘what quantity to choose’ under different market conditions (price-taking, non-price-taking)

Perfect competition in the LR and the SR, what profits look like, how prices move.

Very basic idea of the efficiency of general equilibrium under perfect competition
- When it yields a Pareto-efficient outcome,
- very basically what the first and second welfare theorems mean.
Components of efficiency (top-level, exchange, productive) and what these mean

Market failure (One case: Public goods) (L8)

Consider…

Given what we have learned, (how) will the market provide the goods in this picture?

</aside>

Market failures - public goods, coverage

NS: Ch 16 – public goods section only (skip Lindahl equiliibrium, median voter, single-peaked preferences optional)

Goals of this introduction

How do economists define a public good? What fits into this category?
Better understand ‘market failures’

Market failures

… Occur when prices don’t fully reflect the marginal social benefits or costs

May provide scope for political intervention
How does this happen?

One potential source of market failure: Public Goods

Public Goods (attributes, categories)

What are the characteristics of a public good?

Def – A Pure Public Good is a good that is both

Non-excludable: Once the good is provided, it is impossible/costly to prevent any individual from using/benefiting from it.

Non-rival: One person’s consumption doesn’t reduce the quantity available for others.

The fact that some people use the good doesn’t prevent others from using the same good.
There is no ‘crowding.’
Provision/consumption to additional users at zero marginal (social) cost.

In market economies, private suppliers provide the majority of goods and services to consumers. However, certain goods are publicly provided. These include for example defense, education, and health. Why does the government instead of the market provide these goods? Which characteristics differentiate goods that are privately provided from goods that are publicly provided? How do we define public goods? The terminology might induce the conclusion that ‘—-public goods are good that are publicly provided as opposed to private goods which are privately provided.’ This conclusion is simply WRONG! The public or private nature of the good is an intrinsic characteristic of goods that is not related to the provider of the good Hence, it may well be that the state provides a private good or that the market provides a public good.

In between’s (self-study)

Excludable and rival (depleatable)? $\rightarrow$ Private good

‘Club goods’: excludable but non-rivalrous (at least up to a congestion point).

“Common property”: Nonexcludable but rivalrous

‘Somewhat’ nonexcludable and/or ‘somewhat’ nonrival: $ ightarrow$ ‘impure public goods.’

What about?

Recorded music
‘Information’ goods (e.g., software)
A national park
A theatre performance
Roads
Clean air
Education
Aid to the needy

What about?

Loud music coming from my window
Disease control
Economic research
The justice system
Fireworks in Disney World
The 2012 Olympics in London

The basic ideas

If a good is non-rival then additional provision (of the units produced, to more consumers) is costless.

Thus,

if exclusion is possible, and any positive price is charged, some are deterred from consuming it

this is inefficient: people who could benefit from the good, at no cost to others, will not consume it :(

And…

(If non-rival)

Even if each person provided it for their own benefit (on the assumption that no one else would), they would typically choose too little from a social POV…

Considering their own marginal benefits (and MRS) versus the price or cost, not the social marginal benefit (an ‘externality’ to them)

If a good is non-excludable it will be difficult to charge people for it

many will prefer to wait for others to buy it, and then they enjoy it anyways (free-ride) (that’s a ‘coordination problem’)

But if firms cannot charge for its full value, they might not pay the fixed costs to develop/build/provide it

Who would pay to produce a film that is freely pirated/distributed? Who would pay to develop a drug that must be priced at its marginal cost? Why contribute to police protection for your village, if your neighbours will pay for it anyways?

Motivation

Policy: ‘Public goods argument’ - justifies many government programmes (military, environmental cleanup, research, etc)

Management: Companies/individuals can only profit (or even cover costs) from providing a public good through ???

…gaining subsidies, helping others avoid enforcement (fines) or ???

gaining voluntary support … or ??

by turning it into a private (or excludable) good.

Profit maximisation and supply (L6)

Practical questions

Practical questions

Key goals of this chunk

Key goals of this chunk

Marginal revenue

Marginal revenue

MR for firm facing ‘downward-sloping demand’

Price-taker

MR for a price-taking firm

Profit-maximisation